12.18.16 problem section 9.2, problem 16

Internal problem ID [2130]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 16
Date solved : Monday, January 27, 2025 at 05:42:41 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=14\\ y^{\prime \prime }\left (0\right )&=-40 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 23

dsolve([diff(y(x),x$3)+3*diff(y(x),x$2)-diff(y(x),x)-3*y(x)=0,y(0) = 0, D(y)(0) = 14, (D@@2)(y)(0) = -40],y(x), singsol=all)
 

\[ y = \left (2 \,{\mathrm e}^{4 x}+3 \,{\mathrm e}^{2 x}-5\right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 25

DSolve[{D[y[x],{x,3}]+3*D[y[x],{x,2}]-D[y[x],x]-3*y[x]==0,{y[0]==0,Derivative[1][y][0] ==14,Derivative[2][y][0] ==-40}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -5 e^{-3 x}+3 e^{-x}+2 e^x \]